Answer:
(B) The magnitude is 7sqrt2, and the direction angle is approximately 135 degrees.
Step-by-step explanation:
From the figure, the coordinate of the tail of the vector,
The coordinate of the head of the vector,
The magnitude of a vector is the length between the head and tail of the vector.
By using the distance formula,
the magnitude of the vector 
Now, let 
be the angle made by the vector with the positive direction of the x-axis, so
So, the magnitude of the vector is 
which makes 
with the positive direction of the x-axis.
Hence, option (B) is correct.
Let his total money be x.
He spent (3/7)*x of his money.
He gave 1/4(x-3/7x) to his sister.
which is : (1/4)*(4/7)*x = (1/7)*x
Now,
How much money he have in the beginning =
(3/7)*x+(1/7)*x+120=x
(4/7)*x+120=x
120=x-(4/7)*x
120=(3/7)*x
x=120*7/3 [cross multiplication]
x=280.
So, Alex had $280 in the beginning.
The polynomial is (mx^3+3)(2x²+5x+2)-(8x^5 +20x^4)
if it is reduced to 8x^3+6x²+15x+6, so we can find the value of m
(mx^3+3)(2x²+5x+2)-(8x^5+20x^4) = <span>8x^3+6x²+15x+6
</span>2mx^5+5mx^4+2mx^3+6x²+15x+6-8x^5-20x^4=<span>8x^3+6x²+15x+6
</span>2mx^5+5mx^4+2mx^3=8x^3+6x²+15x+6-6x²-15x-6+ <span>8x^5+20x^4
</span>= 8x^5+20x^4+<span>8x^3= 4(2x^5+5x^4+2x^3)
finally
</span>m(2x^5+5x^4+2x^3)=<span>4(2x^5+5x^4+2x^3), and after simplification
</span>
C: m=4
<span>4. When the expression is factored x²-3x-18 completely,
</span>
one of its factor is x-6
<span>x²-3x-18=0
</span>D= 9-4(-18)= 81, sqrtD=9 x=3-9/2= -6/2= -3, and x=3+9 / 2= 6
so <span>x²-3x-18= (x-6)(x+6)
</span>
Since factors need to show that a number can be divided by another and 6*3=18, C is the answer.
